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In the luminescence processes (Bimolecular process), if long excitation pulses were used, and after a transient initial increase in luminescence intensity, i(t), the steady-state value of intensity is still looks like $$i(0)=\left(\frac{\beta_{\text{r}}}{\beta_{\text{r}}+\beta_{\text{nr}}}\right)G = \left(\frac{\beta_{\text{r}}}{\beta_{\text{r}}+\beta_{\text{nr}}}\right)\alpha I_{\text{ex}} $$

(same like the short excitation pulses). Why?

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